Dynamical phenomena in Fibonacci Semiconductor Superlattices

TL;DR

This paper investigates the complex electron wavepacket dynamics in Fibonacci semiconductor superlattices, revealing wave filtering, fractal energy spectra, and quasiperiodic Bloch oscillations, enhancing understanding of quasiperiodic quantum systems.

Contribution

It provides a detailed analysis of wavepacket propagation, filtering, and oscillations in Fibonacci superlattices, highlighting novel fractal and quasiperiodic phenomena not seen in periodic systems.

Findings

Wavepacket filtering by allowed subminibands

Fractal patterns in transmitted wavepackets

Quasiperiodic Bloch oscillations in Fibonacci superlattices

Abstract

We present a detailed study of the dynamics of electronic wavepackets in Fibonacci semiconductor superlattices, both in flat band conditions and subject to homogeneous electric fields perpendicular to the layers. Coherent propagation of electrons is described by means of a scalar Hamiltonian using the effective-mass approximation. We have found that an initial Gaussian wavepacket is filtered selectively when passing through the superlattice. This means that only those components of the wavepacket whose wavenumber belong to allowed subminibands of the fractal-like energy spectrum can propagate over the entire superlattice. The Fourier pattern of the transmitted part of the wavepacket presents clear evidences of fractality reproducing those of the underlying energy spectrum. This phenomenon persists even in the presence of unintentional disorder due to growth imperfections. Finally, we have demonstrated that periodic coherent-field induced oscillations (Bloch oscillations), which we are able to observe in our simulations of periodic superlattices, are replaced in Fibonacci superlattices by more complex oscillations displaying quasiperiodic signatures, thus sheding more light onto the very peculiar nature of the electronic states in these systems.